Efficient globally optimal consensus maximisation with tree search

Maximum consensus is one of the most popular criteria for robust estimation in computer vision. Despite its widespread use, optimising the criterion is still customarily done by randomised sample-and-test techniques, which do not guarantee optimality of the result. Several globally optimal algorithms exist, but they are too slow to challenge the dominance of randomised methods. We aim to change this state of affairs by proposing a very efficient algorithm for global maximisation of consensus. Under the framework of LP-type methods, we show how consensus maximisation for a wide variety of vision tasks can be posed as a tree search problem. This insight leads to a novel algorithm based on A* search. We propose efficient heuristic and support set updating routines that enable A* search to rapidly find globally optimal results. On common estimation problems, our algorithm is several orders of magnitude faster than previous exact methods. Our work identifies a promising solution for globally optimal consensus maximisation.